Step |
Hyp |
Ref |
Expression |
1 |
|
anass |
⊢ ( ( ( 𝜑 ∧ 𝜓 ) ∧ ( 𝜒 ∧ 𝜃 ) ) ↔ ( 𝜑 ∧ ( 𝜓 ∧ ( 𝜒 ∧ 𝜃 ) ) ) ) |
2 |
|
anass |
⊢ ( ( ( 𝜑 ∧ ( 𝜒 ∧ 𝜃 ) ) ∧ 𝜓 ) ↔ ( 𝜑 ∧ ( ( 𝜒 ∧ 𝜃 ) ∧ 𝜓 ) ) ) |
3 |
|
3anass |
⊢ ( ( 𝜑 ∧ 𝜒 ∧ 𝜃 ) ↔ ( 𝜑 ∧ ( 𝜒 ∧ 𝜃 ) ) ) |
4 |
3
|
anbi1i |
⊢ ( ( ( 𝜑 ∧ 𝜒 ∧ 𝜃 ) ∧ 𝜓 ) ↔ ( ( 𝜑 ∧ ( 𝜒 ∧ 𝜃 ) ) ∧ 𝜓 ) ) |
5 |
|
ancom |
⊢ ( ( 𝜓 ∧ ( 𝜒 ∧ 𝜃 ) ) ↔ ( ( 𝜒 ∧ 𝜃 ) ∧ 𝜓 ) ) |
6 |
5
|
anbi2i |
⊢ ( ( 𝜑 ∧ ( 𝜓 ∧ ( 𝜒 ∧ 𝜃 ) ) ) ↔ ( 𝜑 ∧ ( ( 𝜒 ∧ 𝜃 ) ∧ 𝜓 ) ) ) |
7 |
2 4 6
|
3bitr4ri |
⊢ ( ( 𝜑 ∧ ( 𝜓 ∧ ( 𝜒 ∧ 𝜃 ) ) ) ↔ ( ( 𝜑 ∧ 𝜒 ∧ 𝜃 ) ∧ 𝜓 ) ) |
8 |
1 7
|
bitri |
⊢ ( ( ( 𝜑 ∧ 𝜓 ) ∧ ( 𝜒 ∧ 𝜃 ) ) ↔ ( ( 𝜑 ∧ 𝜒 ∧ 𝜃 ) ∧ 𝜓 ) ) |